I present experiments with ultracold atoms which demonstrate a novel avenue to study strongly correlated physics with atomic quantum gases. Interacting fermionic quantum gases are essential for the understanding of solid state materials. By creating a quantum degenerate Fermi gas in a three-dimensional optical lattice a new window to the physics of correlated many-body systems is opened. Important physical quantities that describe these systems, such as the Fermi surface and the on-site correlation functions are directly measured. The interactions between different spin states are tunable by exploiting a magnetically induced Feshbach resonance. An interaction-driven coupling between different Bloch bands and the conversion of pairs of fermionic atoms into bosonic molecules have been observed. The regime of low-dimensional quantum gases is accessed by employing anisotropic optical lattices. One-dimensional quantum gases interacting by both s-wave and pwave interactions have been realized and studied. Of particular interest have been the effects of the strong confinement of the atoms on the atomic interactions. We have observed the existence of molecules where the bound state is stabilized only by the presence of a strong confining potential. The detection of correlations between neutral atoms poses a significant experimental challenge. We have realized a detection scheme for individual atoms from a quantum degenerate atom source which allows for the direct measurement of atomatom correlations in a Hanbury Brown and Twiss setup. We have measured the second order correlation function of an atom laser beam extracted from a Bose-Einstein condensate and find the intensity correlation function to be equal unity. This distinguishes the coherent atom laser beam from thermal atomic beams which exhibit larger intensity fluctuations due to quantum statistics. These experiments demonstrate the unprecedented versatility of creating and detecting correlated quantum states with ultracold atomic gases. The very controlled study of strongly correlated phases and the unparalleled direct measurement of correlation functions opens up new perspectives onto fundamental questions of modern quantum many-body physicsShow more